with \({\rm St}\)  the standard representation and \(j\)  and \(k\)  integers
with \(j\ge 0\) .
We call the weight \((j,k)\) .
We have the notion of cusp forms and \(S_{j,k}=S_{j,k}(\Gamma _2)\) 
denotes the vector space
of cusp forms of weight \((j,k)\) . For \(j=0\)  we are dealing with
scalar-valued Siegel modular forms. We also have an algebra of operators, the Hecke
algebra with operators \(T_p\)  for every prime \(p\) ; see for example
[1]} and the references there. Scalar-valued Siegel modular forms of degree
2 were studied by Igusa in the 1960s [2]}, [3]}.
Igusa determined the ring of scalar-valued modular forms of degree 2.
Satoh was one of the first
to study vector-valued ones [4]}.
